It can mean either. Sometimes you can put "det/den/de der" to mean "that" but normally only context and the tone of voice are the ways you can tell them apart. Both "that other house" and "the other house" should be accepted
Thanks, Xneb. "... the other house ..." was not accepted, but I get the point of this lesson, and why it wasn't. Maybe pictures of people (or penguins, sharks, turtles) pointing could help to give it context.